Elektriksel olarak büyük yalıtkan kaplı metal silindirdeki yüzey dalgaları için asimptotik kapalı ifadeler

ABSTRACTAN ASYMPTOTIC CLOSED-FORM PARAXIALFORMULATION FOR SURFACE FIELDS ONELECTRICALLY LARGE DIELECTRIC COATEDCIRCULAR CYLINDERSTuncay ErdüloM.S. in Electrical and Electronics EngineeringSupervisor: Assist. Prof. Dr. Vakur B. Ertü rkuAugust, 2005Investigation of surface fields excited on material coated perfectly conducting(PEC) circular cylinders is a problem of interest (i) due to its application in thedesign and analysis of conformal microstrip antennas and arrays, and (ii) it actsas a canonical problem useful toward the development of asymptotic solutionsvalid for arbitrarily convex material coated smooth surfaces. Nevertheless, in-tegral equation based solutions that use the eigenfunction representation of theappropriate dyadic Green?s function, as well as pure numerical solutions becomeintractable when the geometry of interest is electrically large. A few asymptoticsolutions have been suggested in the literature to overcome this problem. How-ever, these solutions are not accurate within the paraxial (nearly axial) region ofthe cylinder. This is a well known problem that has been observed for PEC andimpedance cylinders in the past as well. Recently, a novel paraxial space-domainrepresentation for the surface fields has been presented by Ertü rk et. al. (IEEEuTrans. Antennas and Propagat., 11, 1577-1587, 2002), which is much faster thanthe well-known eigenfunction solution. However, in this representation the fi-nal expressions for the surface fields have some special functions which involveSommerfeld type integrals to be evaluated numerically.In this thesis, using the final results of this paraxial space-domain formula-tion as a starting point, a relatively simple closed-form asymptotic representationfor the surface fields of a dielectric coated, electrically large circular cylinder isdeveloped. The large parameter in this asymptotic development is the separa-tion between the source and observation points. The solution uses the fact that1existing special functions in the previously developed paraxial formulation are insimilar forms when compared to the special functions used in the Sommerfeldintegral representation for the single layer microstrip dyadic Green?s function forthe planar case. Furthermore, when the radius of the cylinder goes to infinity,using the leading terms of Debye representations for the Hankel and Bessel func-tions (as well as their derivatives), cylindrical special functions recover their pla-nar counterparts. Therefore, first a steepest descent path representation of thesespecial functions is obtained. Then, using the method suggested by Barkeshliet. al. (IEEE Trans. Antennas and Propagat., 9, 1374-1383, 1990) closed-formexpressions are achieved.Numerical results in the form of mutual coupling between two tangential elec-tric current modes have been obtained using these closed-form expressions andcompared with the previously developed paraxial formulation as well as eigenfunc-tion solution to assess the accuracy and efficiency of these closed-form solutions.Details of the formulation is presented.Keywords: Coated cylinders, Green?s function, asymptotic, paraxial.2